The reason that you hear the '-r-r-r' noise is due to the high bypass ratio fan (N1) being at the front of
the engine. This fan is turned by the power section(N2) of the engine and in turn "sucks" more air into the
inlet the faster it turns. This is known as a "tractor fan", or air pulling unit, thus the N1 fan blades making
the noise you hear. Most all high bypass fan engines make this noise to some extent.
Yes, all jet engines and especially high BPR ones have some fan noise (ever stand in front of a jet that doesn't have stator vanes in front of the first fan/compressor stage?

) but I don't think that is what the question was about.
The A320s has this distinctive sound that is hard to describe. During my first week or two on the ramp I sometimes looked up to see what kind of turboprop it was that let out so much noise from it's jet cores - and was surprised to see a 320 on the takeoff roll.
As to the cause of that sound, well, I have no idea. Perhaps a beat frequency caused by slightly different N1 speeds on #1 and #2 and some kind of soundwaves generated at the fan blade tips? Does anyone know?
Cheers,
/ft